Portability | non-portable (multi-param classes, functional dependencies) |
---|---|

Stability | experimental |

Maintainer | libraries@haskell.org |

Lazy state monads.

This module is inspired by the paper /Functional Programming with Overloading and Higher-Order Polymorphism/, Mark P Jones (http://web.cecs.pdx.edu/~mpj/) Advanced School of Functional Programming, 1995.

- class Monad m => MonadState s m | m -> s where
- modify :: MonadState s m => (s -> s) -> m ()
- gets :: MonadState s m => (s -> a) -> m a
- type State s = StateT s Identity
- runState :: State s a -> s -> (a, s)
- evalState :: State s a -> s -> a
- execState :: State s a -> s -> s
- mapState :: ((a, s) -> (b, s)) -> State s a -> State s b
- withState :: (s -> s) -> State s a -> State s a
- newtype StateT s m a = StateT {
- runStateT :: s -> m (a, s)

- evalStateT :: Monad m => StateT s m a -> s -> m a
- execStateT :: Monad m => StateT s m a -> s -> m s
- mapStateT :: (m (a, s) -> n (b, s)) -> StateT s m a -> StateT s n b
- withStateT :: (s -> s) -> StateT s m a -> StateT s m a
- module Control.Monad
- module Control.Monad.Fix
- module Control.Monad.Trans

# MonadState class

class Monad m => MonadState s m | m -> s whereSource

*get* returns the state from the internals of the monad.

*put* replaces the state inside the monad.

MonadState s m => MonadState s (MaybeT m) | |

MonadState s m => MonadState s (ListT m) | |

MonadState s m => MonadState s (IdentityT m) | |

(Monoid w, MonadState s m) => MonadState s (WriterT w m) | |

(Monoid w, MonadState s m) => MonadState s (WriterT w m) | |

MonadState s m => MonadState s (ReaderT r m) | |

(Error e, MonadState s m) => MonadState s (ErrorT e m) | |

MonadState s m => MonadState s (ContT r m) | |

Monad m => MonadState s (StateT s m) | |

Monad m => MonadState s (StateT s m) | |

(Monad m, Monoid w) => MonadState s (RWST r w s m) | |

(Monad m, Monoid w) => MonadState s (RWST r w s m) |

modify :: MonadState s m => (s -> s) -> m ()Source

Monadic state transformer.

Maps an old state to a new state inside a state monad. The old state is thrown away.

Main> :t modify ((+1) :: Int -> Int) modify (...) :: (MonadState Int a) => a ()

This says that `modify (+1)`

acts over any
Monad that is a member of the `MonadState`

class,
with an `Int`

state.

gets :: MonadState s m => (s -> a) -> m aSource

Gets specific component of the state, using a projection function supplied.

# The State monad

type State s = StateT s Identity

A parameterizable state monad where *s* is the type of the state
to carry and *a* is the type of the *return value*.

:: State s a | The state to evaluate |

-> s | An initial value |

-> a | The return value of the state application |

Evaluate this state monad with the given initial state,throwing
away the final state. Very much like `fst`

composed with
`runstate`

.

:: State s a | The state to evaluate |

-> s | An initial value |

-> s | The new state |

Execute this state and return the new state, throwing away the
return value. Very much like `snd`

composed with
`runstate`

.

mapState :: ((a, s) -> (b, s)) -> State s a -> State s b

Map a stateful computation from one (return value, state) pair to another. For instance, to convert numberTree from a function that returns a tree to a function that returns the sum of the numbered tree (see the Examples section for numberTree and sumTree) you may write:

sumNumberedTree :: (Eq a) => Tree a -> State (Table a) Int sumNumberedTree = mapState (\ (t, tab) -> (sumTree t, tab)) . numberTree

withState :: (s -> s) -> State s a -> State s a

Apply this function to this state and return the resulting state.

# The StateT monad transformer

newtype StateT s m a

A parameterizable state monad for encapsulating an inner monad.

The StateT Monad structure is parameterized over two things:

- s - The state.
- m - The inner monad.

Here are some examples of use:

(Parser from ParseLib with Hugs)

type Parser a = StateT String [] a ==> StateT (String -> [(a,String)])

For example, item can be written as:

item = do (x:xs) <- get put xs return x type BoringState s a = StateT s Identity a ==> StateT (s -> Identity (a,s)) type StateWithIO s a = StateT s IO a ==> StateT (s -> IO (a,s)) type StateWithErr s a = StateT s Maybe a ==> StateT (s -> Maybe (a,s))

MonadWriter w m => MonadWriter w (StateT s m) | |

Monad m => MonadState s (StateT s m) | |

MonadReader r m => MonadReader r (StateT s m) | |

MonadError e m => MonadError e (StateT s m) | |

MonadTrans (StateT s) | |

Monad m => Monad (StateT s m) | |

Functor m => Functor (StateT s m) | |

MonadFix m => MonadFix (StateT s m) | |

MonadPlus m => MonadPlus (StateT s m) | |

(Functor m, Monad m) => Applicative (StateT s m) | |

(Functor m, MonadPlus m) => Alternative (StateT s m) | |

MonadIO m => MonadIO (StateT s m) | |

MonadCont m => MonadCont (StateT s m) |

evalStateT :: Monad m => StateT s m a -> s -> m a

Similar to `evalState`

execStateT :: Monad m => StateT s m a -> s -> m s

Similar to `execState`

withStateT :: (s -> s) -> StateT s m a -> StateT s m a

Similar to `withState`

module Control.Monad

module Control.Monad.Fix

module Control.Monad.Trans

# Examples

A function to increment a counter. Taken from the paper
*Generalising Monads to Arrows*, John
Hughes (http://www.math.chalmers.se/~rjmh/), November 1998:

tick :: State Int Int tick = do n <- get put (n+1) return n

Add one to the given number using the state monad:

plusOne :: Int -> Int plusOne n = execState tick n

A contrived addition example. Works only with positive numbers:

plus :: Int -> Int -> Int plus n x = execState (sequence $ replicate n tick) x

An example from *The Craft of Functional Programming*, Simon
Thompson (http://www.cs.kent.ac.uk/people/staff/sjt/),
Addison-Wesley 1999: "Given an arbitrary tree, transform it to a
tree of integers in which the original elements are replaced by
natural numbers, starting from 0. The same element has to be
replaced by the same number at every occurrence, and when we meet
an as-yet-unvisited element we have to find a 'new' number to match
it with:"

data Tree a = Nil | Node a (Tree a) (Tree a) deriving (Show, Eq) type Table a = [a]

numberTree :: Eq a => Tree a -> State (Table a) (Tree Int) numberTree Nil = return Nil numberTree (Node x t1 t2) = do num <- numberNode x nt1 <- numberTree t1 nt2 <- numberTree t2 return (Node num nt1 nt2) where numberNode :: Eq a => a -> State (Table a) Int numberNode x = do table <- get (newTable, newPos) <- return (nNode x table) put newTable return newPos nNode:: (Eq a) => a -> Table a -> (Table a, Int) nNode x table = case (findIndexInList (== x) table) of Nothing -> (table ++ [x], length table) Just i -> (table, i) findIndexInList :: (a -> Bool) -> [a] -> Maybe Int findIndexInList = findIndexInListHelp 0 findIndexInListHelp _ _ [] = Nothing findIndexInListHelp count f (h:t) = if (f h) then Just count else findIndexInListHelp (count+1) f t

numTree applies numberTree with an initial state:

numTree :: (Eq a) => Tree a -> Tree Int numTree t = evalState (numberTree t) []

testTree = Node "Zero" (Node "One" (Node "Two" Nil Nil) (Node "One" (Node "Zero" Nil Nil) Nil)) Nil numTree testTree => Node 0 (Node 1 (Node 2 Nil Nil) (Node 1 (Node 0 Nil Nil) Nil)) Nil

sumTree is a little helper function that does not use the State monad:

sumTree :: (Num a) => Tree a -> a sumTree Nil = 0 sumTree (Node e t1 t2) = e + (sumTree t1) + (sumTree t2)